Problem: Simplify the following expression: $x = \dfrac{6z^2 + 48z + 42}{z + 7} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ x =\dfrac{6(z^2 + 8z + 7)}{z + 7} $ Then we factor the remaining polynomial: $z^2 + {8}z + {7} $ ${7} + {1} = {8}$ ${7} \times {1} = {7}$ $ (z + {7}) (z + {1}) $ This gives us a factored expression: $\dfrac{6(z + {7}) (z + {1})}{z + 7}$ We can divide the numerator and denominator by $(z - 7)$ on condition that $z \neq -7$ Therefore $x = 6(z + 1); z \neq -7$